Robust H∞ filter design with pole constraints for discrete-time systems

The problem of full-order guaranteed cost H∞ filtering design for discrete-time systems with polytope type uncertainty is investigated in this paper. The main purpose is to obtain a stable and proper linear filter such that the filtering error system remains robustly stable within a prespecified H∞ attenuation level. Sufficient conditions for the existence of such robust filter are provided in terms of linear matrix inequalities, which can be efficiently solved by means of high-performance convex optimization procedures with global convergence assured. Moreover, as an improvement, the filter dynamics can be constrained to some specific regions inside the unit open disk.